Linear Codes over ${\mathbb{F}}_q[x]/(x^2)$ and $GR(p^2,m)$ Reaching the Griesmer Bound

Jin Li, Aixian Zhang, Keqin Feng

We construct two series of linear codes over finite ring ${\mathbb{F}}_q[x]/(x^2)$ and Galois ring $GR(p^2,m)$ respectively reaching the Griesmer bound. They derive two series of c…